Probabilistic Model Predictive Control for Mineral Flotation using Gaussian Processes

Recent advancements in machine learning and time series analysis have opened new avenues for improving predictive control in complex systems such as mineral flotation. Techniques leveraging multivariate predictive control in mineral flotation have seen significant progress in recent years. However, challenges in developing an accurate dynamic model that encapsulates both the pulp and froth phases have hindered further advancements. Now, with a readily available model containing equations that describe the physics of flotation froths, an opportunity for novel control strategies presents itself. In this study, a Gaussian Process (GP) Model Predictive Control (MPC) strategy is proposed to integrate uncertainty quantification directly into the control framework. By leveraging the probabilistic nature of GP models, this approach captures process variability and adapts dynamically to new data, ensuring continuous refinement of the GP model within the MPC strategy. Unlike previous implementations where model parameters remained static, this methodology updates the GP model in real time, allowing for improved decision-making in the face of process uncertainty. The GP model was trained, optimized with JAX, evaluated using relevant metrics, and implemented as a surrogate within the MPC framework. The results demonstrate the capability of the GP model to accurately represent process dynamics while minimising prediction errors. Moreover, incorporating uncertainty reduction through standard deviation minimisation in the objective function enhances both control performance and system robustness. This paper sets the basis for the potential of using GP-MPC to enhance both the accuracy and robustness of mineral froth flotation control.